In recent years, there have been proposed and developed various variable displacement pumps capable of varying a discharge of working fluid, usually expressed as a fluid flow rate per one revolution of a pump rotor. A variable displacement pump of this type has been disclosed in Japanese Patent Provisional Publication No. 2009-92023 (hereinafter is referred to as “JP2009-092023”) assigned to the assignee of the present invention. In the variable displacement vane pump disclosed in JP2009-092023, its discharge is variably adjusted by changing an eccentricity of the geometric center of a cylinder bore of a cam ring with respect to the axis of rotation of a vane rotor. One end of the cam ring is pivoted on a pump housing. The vane rotor is accommodated in an inner periphery of the cam ring and driven by torque transmitted from an engine crankshaft. A plurality of vanes are fitted into an outer periphery of the rotor in a manner so as to radially slide from the rotor toward the inner peripheral surface of the cam ring, and laid out to be kept in abutted-engagement with the inner peripheral surface of the cam ring. The vanes are configured to define a plurality of variable-volume pump working chambers in cooperation with the outer peripheral surface of the rotor, the inner peripheral surface of the cam ring, and two axially opposed sidewalls facing both sides of the cam ring respectively. Also provided is a double-spring biasing device comprised of inner and outer coil springs and configured to force the cam ring in a direction that the volume difference between a volume of the largest working chamber and a volume of the smallest working chamber increases, in other words, in a direction that the eccentricity of the cam ring with respect to the rotation center of the vane rotor increases. The double-spring biasing device disclosed in JP2009-092023 is laid out to produce a nonlinear spring characteristic that a spring constant discontinuously increases, as the amount of oscillating motion (pivotal motion) of the cam ring increases in a direction that the volume difference between a volume of the largest working chamber and a volume of the smallest working chamber decreases, thereby ensuring a two-stage pump flow rate characteristic.